Orthogonal frequency-division multiplexing (OFDM) is being widely used in the physical layer specifications, such as IEEE 802.11a, IEEE 802.16a, and HIPERLAN/2, of many broadband wireless access systems. Particularly, IEEE 802.11a, providing data rates ranging from 6 Mbits/s to 54 Mbits/s by a link adaptation scheme with different modulation formats from binary phase shift keying (BPSK) to 64-ary quadrature amplitude modulation (64-QAM), has become a popular computer industry standard for wireless network cards. It is also being used in digital audio broadcasting (DAB) and digital video broadcasting (DVB) systems in Europe. Moreover, AT&T Labs recently demonstrated their fourth-generation (4G) system with OFDM technology for the downlink. OFDM technology can find its way to these applications because of its wideband nature and the ability to effectively convert a frequency selective fading channel into several nearly flat fading channels.
In discrete Fourier transform (DFT) OFDM, intersymbol interference (ISI) can be completely canceled by using the cyclic prefix (CP) scheme provided the CP is longer than the channel impulse response (CIR). See A. Peled and A. Ruiz, “Frequency domain data transmission using reduced computational complexity algorithms,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, 1980, pp. 964-967. In addition, if the carrier frequency is synchronized perfectly, and the CIR does not vary in one OFDM frame, there will be no intercarrier interference (ICI) components in the received signals. Therefore, one can use a one-tap equalizer in the receiver to compensate the channel distortion. Actually, the CP scheme works because of the fact that the DFT of the circular convolution of two sequences is equal to the multiplication of the DFTs of these two sequences. See A. V. Oppenheim, R. W. Schafer, with J. R. Buck, Discrete-Time Signal Processing, 2nd Ed., Prentice Hall, 1998. DFT-OFDM can not guarantee symbol recovery if the channel transfer function has zero(s) on the FFT grid.
As an alternative to use of the CP, a zero padding (ZP) scheme can be used in DFT-OFDM. A ZP scheme can provide ISI-free transmission if the length of channel impulse response is less than the length of the ZP. This scheme ensures symbol recovery regardless of the channel zero locations.
The above mentioned systems are discrete Fourier transform (DFT)-based multicarrier modulations (MCMs) where the complex exponential functions set is employed as an orthogonal basis.
An alternative to a DFT-based OFDM system is a system employing another orthogonal basis, namely a single set of cosinusoidal functions cos(2πnFΔt) where n=0, 1, . . . , N−1 and 0≦t<T, to implement the multicarrier modulation scheme. The minimum FΔ required to satisfy the orthogonality condition
                                          ∫            0            T                    ⁢                                                    2                T                                      ⁢                          cos              ⁡                              (                                  2                  ⁢                  π                  ⁢                                                                          ⁢                  k                  ⁢                                                                          ⁢                                      F                    Δ                                    ⁢                  t                                )                                      ⁢                                          2                T                                      ⁢                          cos              ⁡                              (                                  2                  ⁢                  π                  ⁢                                                                          ⁢                  m                  ⁢                                                                          ⁢                                      F                    Δ                                    ⁢                  t                                )                                      ⁢                          ⅆ              t                                      =                  {                                                                      1                  ,                                                                              k                  =                  m                                                                                                      0                  ,                                                                              k                  ≠                  m                                                                                        (        1        )            is ½ T Hz. This scheme can be synthesized using a discrete cosine transform (DCT). This scheme will be denoted as DCT-OFDM, and the conventional OFDM system as DFT-OFDM. As far as fast implementation algorithms are concerned, the fast DCT algorithms proposed in W. H. Chen, C. H. Smith, and S. C. Fralick; “A fast computational algorithm for the discrete cosine transform,” IEEE Trans. Commun., vol. 25, pp. 1004-1009, September 1977 and Zhongde Wang, “Fast algorithms for the discrete w transform and for the discrete Fourier transform,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, pp. 803-816, August 1984 could provide fewer computational steps than fast Fourier transform (FFT) algorithms.
Unfortunately, in general, the DCT does not have the circular convolution multiplication property. Inserting the CP scheme directly into the proposed DCT-OFDM system does eliminate ISI. However, as a side effect, ICI is introduced even when the CIR does not change in one DCT-OFDM frame.
In K. R. Rao, P. Yip, Discrete Cosine Transform. Academic Press, 1990 and S. A. Martucci, “Symmetric convolution and the discrete sine and cosine transform,” IEEE Trans. Signal Processing, vol. 42, pp. 1038-1051, May 1994 it was suggested that when the given sequences are evenly symmetrically extended, a circular convolution property similar to the DFT can be found. By employing this property, a DCT-based OFDM system is proposed in G. D. Mandyam, “On the discrete cosine transform and OFDM systems,” in Proc. ICASSP 2003, pp. 544-547. However, the symmetric extension of the original data sequence reduces the data transmission efficiency by at least one-half.